We study the marriage problem where a probability distribution over matchings is chosen. The “core” has been central to the the analysis of the deterministic problem. This is particularly the case since it coincides with the (conceptually) simpler set of “stable” matchings.
While the generalization of stability to the probabilistic stetting in an ex post sense is clear (Rothblum 1992), there are several natural ex ante generalizations: expected utility for given von Neumann-Morgenstern preferences, stochastic dominance requiring comparability, and stochastic dominance without requiring comparability.
The purpose of this paper is to work out the logical relations between the various concepts. Thus, we provide a foundation for further research on probabilistic matching.
Vikram Manjunath